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Designs, Codes and Cryptography

Erschienen in:

01.10.2018

Dense families of modular curves, prime numbers and uniform symmetric tensor rank of multiplication in certain finite fields

verfasst von: Stéphane Ballet, Alexey Zykin

Erschienen in: Designs, Codes and Cryptography | Ausgabe 2-3/2019

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Abstract

We obtain new uniform bounds for the symmetric tensor rank of multiplication in finite extensions of any finite field \(\mathbb {F}_p\) or \(\mathbb {F}_{p^2}\) where p denotes a prime number \(\ge 5\). In this aim, we use the symmetric Chudnovsky-type generalized algorithm applied on sufficiently dense families of modular curves defined over \(\mathbb {F}_{p^2}\) attaining the Drinfeld–Vladuts bound and on the descent of these families to the definition field \(\mathbb {F}_p\). These families are obtained thanks to prime number density theorems of type Hoheisel, in particular a result due to Dudek (Funct Approx Commmentarii Math, 55(2):177–197, 2016).

Vorheriger Artikel Local distributions for eigenfunctions and perfect colorings of q-ary Hamming graph

Nächster Artikel Evaluating Bernstein–Rabin–Winograd polynomials

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Titel: Dense families of modular curves, prime numbers and uniform symmetric tensor rank of multiplication in certain finite fields
verfasst von: Stéphane Ballet
Alexey Zykin
Publikationsdatum: 01.10.2018
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 2-3/2019
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-018-0560-8

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